Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decid

Question

Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. If the test predicts that there is no oil, what is the probability after the test that the land has oil?

0

Answers ( No )

    0
    2021-09-09T01:32:01+00:00

    The options are

    A.

    0.1698

    B.

    0.2217

    C.

    0.5532

    D.

    0.7660

    0
    2021-09-09T01:32:10+00:00

    Answer: The probability after the test that the land has oil is 0.09.

    Explanation:

    Let A is the event that the land has oil.

    It is given that there is a 45% chance that the land has oil. So,

    P(A)=\frac{45}{100}

    The probability that the land has no oil is,

    P(A)=[tex]P(A')=1-P(A)=1-\frac{45}{100}=\frac{100-45}{100}=\frac{55}{100}

    Let B is the event that the kit gives the accurate rate of indicating oil in the soil. So,

    P(B)=\frac{80}{100}

    The probability that the kit gives the false result is,

    P(B')=1-P(B)=1-\frac{80}{100}=\frac{100-80}{100}=\frac{20}{100}

    Events A and B are two independent events and we have to find the probability that the last has oil and kit given false result.

    P(A\cap B')=P(A)P(B')

    P(A\cap B')=(\frac{45}{100})(\frac{20}{100})=\frac{900}{10000} =\frac{9}{100}=0.09

    Therefore, the if the test predicts that there is no oil, then the probability after the test that the land has oil is 0.09.

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